What will change and what will remain

This is a continuation of the two articles “What needs to be agreed upon” and “What can be disagreed upon”, in which two people have a discussion, after which a third party is invited to interpret a transcription of it. We have concluded that if the meaning of a posit is universally agreed upon, anyone is nevertheless at liberty to disagree or express doubt towards what it is saying. Opinions about posits are recorded in the transcript itself using assertions, a kind of meta-posit that assigns someone’s confidence level with respect to a posit.

Change is everywhere, and the last article concluded that both the circumstances that posits and assertions describe may change over time. Values change and opinions change. Let us make the transcript a living document, required to capture such changes. Additionally, the transcript much be historically complete, capturing the changes in a non-destructive manner. Anything that goes into the transcript is written in stone.

Grab your chisel, because Jennifer broke up with her boyfriend. Recall that the posit P1 is ({(J42, girlfriend), (B43, boyfriend)}, official, 2019), where J42 is Jennifer and B43 her boyfriend. The posit P3 tells us what happened in 2020 and it looks like this ({(J42, girlfriend), (B43, boyfriend)}, broken up, 2020). Remember the posit P2? It is ({(J42, nickname)}, Jen, 1988). Clearly, they are all different posits, P1 ≠ P2 ≠ P3, but P1 and P3 must share something in order for them to be describing a change that they do not share with P2.

It is actually possible to precisely define change. When two posits share the same set in their first position, but have different values and one time point follows the other, they describe a change. With that in place, P3 is obviously a change from P1. Since the set in P2 differs from that in P1 and P2, it is not a change of either P1 or P3. In #transitional modeling, the set is called an appearance set. They remain, indefinitely, while their surroundings may change entirely. Even after J42 is gone, the dereferencing sets in which that identity is found will remain, because we can, of course, have a recollection of things that are no more.

Then how does change affect assertions? Since assertions are posits themselves it works in exactly the same way. Jennifer made the following assertion on the 5th of April in 2019 ({(P1, posit), (J42, determines confidence)}, 0.8, 2019-04-05), stating that it is very likely that she and her boyfriend officially has been an item since 2019. After learning that her “boyfriend” thought otherwise, she changed her mind. Let’s say that they had a serious talk about this on the 21st of September 2019. Jennifer’s revised confidence in P1 can then be expressed through another assertion ({(P1, posit), (J42, determines confidence)}, 0, 2019-09-21). This assertion changes her previous confidence level from 0.8 to 0, so after the 21st she has no clue if they actually were an item or not.

Incidentally, this is how a ‘logical delete’ works in a bitemporal database. Albeit, in those databases there are only two confidence values, 1 (recorded) and 0 (deleted). The database itself is also the only one allowed to have an opinion. In other words, the functionality of a bitemporal database can be described as a small subset of #transitional modeling. When confidences are extended to the continuous interval [0, 1], the functionality approaches that of probabalistic databases. If further extended to include negative confidence, [-1, 1], we approach uncertainty theory, yet to be explored in databases. The fact that anyone may have an opinion is similar to multi-tenant databases. Transitional modeling as a formal base is very powerful, despite it’s simple construction.

Back in the shoes of the third party reading the transcript, we find the posit P4 as ({(S44, nickname)}, Jen, 1988). So, wait, what? There were in fact two different Jens after all, J42 and S44? What exactly is the thing with identity S44? This will be the topic of the next article, entitled “What we are”.

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Lars Rönnbäck

Co-developer of the Anchor Modeling technique. Programmer of the online modeling tool. Site maintainer. Presenter and trainer.

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